Using a small melon baller or spoon, scoop two-thirds of the way down into one of the 2-inch pieces of cucumber, forming a cucumber shot glass. Refrigerate until ready to use.
Muddle the grape tomatoes, 4 of the basil leaves and remaining cucumber piece in a cocktail shaker until well crushed. Add the vodka, vinegar, lemon juice and some ice to the cocktail shaker and shake until well mixed. Strain into the cucumber shot glass and garnish with the remaining basil leaf.